### Instantons in complex geometry: PDF files with the talks

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Monads appear in a wide variety of context within Algebraic
Geometry.
We will focus our attention on linear monads as a tool for
constructing indecomposable vector bundles on hyperquadrics and on the
particular case of instanton bundles on them. This is a joint work with
R.M. Miro-Roig.

I will talk about moduli spaces of framed perverse instantons on P^3.
As an open subset they contain the moduli space of framed instantons
studied by I. Frenkel and M. Jardim. I will explain the connection
with the moduli space of pairs on the blow up of P^3 along a line.
I will also study the map between the Gieseker and Donaldson-Uhlenbeck
partial compactifications of the moduli space of instantons on P^3.
Finally I will construct a few counterexamples to earlier
conjectures and results concerning these moduli spaces.

In my talk, I will address the problem of giving a cohomological characterization of vector bundles
on algebraic varieties. This is a longstanding problem in Algebraic Geometry which has its roots
in an old paper by Horrocks where he gave a cohomological characterization of line bundles on
projective spaces P^n.
In my talk, I will give a cohomological characterization of the bundle of p-differential forms on
multiprojective spaces P^{n_1}\times ... \times P^{n_s} and a cohomological characterization of Steiner bundles on
algebraic varieties. As a main tool I will use a generalized version of Beilinson's spectral sequence.

This is joint work with Costa and Soares

In this talk, I will first review the "classical" formalism of quiver
representations, with a view on sheaves and instantons on projective
manifolds. Then, I will give a survey on results on quiver bundles on
projective manifolds and their moduli spaces. At the end, I will present
joint work with Garcia-Prada and Heinloth on the motive of the moduli
space of Higgs bundles of rank four and odd degree on a compact Riemann
surface.

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